The”standard-siren” approaches of gravitational wave cosmology appeal to the luminosity distance estimation from the GW observation which relies on the fine details of the waveform. We propose a new waveform independent strategy based on the systems where strongly lensed gravitational waves (GWs) and their electromagnetic (EM) counterparts can be detected simultaneously. With the images and redshifts observed in the EM domain combined with very precise measurements of time delays from lensed GW signals, we can achieve precise cosmography in the era of third-generation gravitational-wave detectors. In particular we demonstrate that the uncertainty of the Hubble constant $H_0$ determination from just $10$ such systems can decrease to $\sim0.4\%$ in a flat $\Lambda$CDM universe.